Year 10 - Maths
Calculating arc length
2D and 3D shape: compound shapes
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit, knowledge of circles and polygons is drawn upon to find the arc length and area of a circle sector and areas of complex compound shapes.
Lesson Summary
You will learn to calculate the arc length of a sector and the sector's perimeter.
Key Notes
- Using fractions, you can calculate part of the circumference.
- This gives the length of the curved section of a sector.
- To find the perimeter, you will need to add the radius twice.
- An exact answer may be given in terms of π
Vocabulary To Learn
- Arc: An arc is part of a curve. An arc of a circle is part of the circle's circumference.
- Sector: A sector is the region formed between two radii and their connecting arc.
- Chord: A chord is any line segment joining two points on the circumference of a circle.
- Radius: The radius is any line segment that joins the centre of a circle to any point on its circumference.
- Circumference: The circumference of a circle is the perimeter of the circle.
Common Mistakes To Avoid
- "When finding the perimeter of a sector, I need to multiply the radius by a fraction of a full circle, just like I did with the circumference to find the arc length."
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Using fractions, you can calculate part of the circumference. This gives the length of the curved section of a sector.
2. Use this key word in a maths sentence and explain it clearly. 'Arc'
An arc is part of a curve. An arc of a circle is part of the circle's circumference. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: "When finding the perimeter of a sector, I need to multiply the radius by a fraction of a full circle, just like I did with the circumference to find the arc length.". Correction: Reminder that only part (the arc length) of the formula for perimeter of a sector varies with the angle. A desmos or geogebra model can help to show this.
More Lessons In This Unit
- Area of a sector Study Guide
- Area of compound shapes Study Guide
- Checking and securing understanding of area for compound shapes Study Guide
- Checking and securing understanding of area for standard shapes Study Guide
- Checking and securing understanding of circles Study Guide
- Checking and securing understanding of converting between metric and imperial measures Study Guide
- Checking and securing understanding of perimeter for compound shapes Study Guide
- Checking and securing understanding of perimeter for standard shapes Study Guide
- Checking and securing understanding of scales and conversion Study Guide
- Equations from complex shapes Study Guide
- Perimeter and area in a contextual setting Study Guide
- Problem solving with 2D shapes Study Guide
- Problem solving with complex 2D shapes Study Guide
- Shapes on coordinate grids Study Guide
- Shapes within shapes Study Guide
Browse all guides in the Year 10 Maths guide library.